When you fire on the Prophecy pretty much everything aggros except the Prophecy may not aggro.
Firing on the Prophecy causes a spawn of:
4x Elite Frigates (This group will also spawn after a certain time even if you haven't attacked the Prophecy. Estimate approx 20min.)

There are 6 mines at jump in 22km - 70km away.
After one mine explodes 4 new mines spawn. After shooting 4 more mines there's another spawn of 4 mines + the "Amarrian drone mine 1".
After blowing up "Amarrian drone mine 1" the mission is over.

Upon firing on the Mines, 4 Amarr Smart Drone NPCs (Rogue Drone Battlecruisers) will appear around the mine, and your ship (and any in your fleet on the grid) will take 600-1000 damage. Destroy the drones after each mine to avoid being swamped.

For snipers: snipe all of the mines from as far away as you can. Keep shooting the mines until the "Amarrian drone mine 1" spawns. Blow that one up, and mission completed. (Note: When I did the mission Drones didn't attack until blowing up the last 3 mines - NikalVaszol.) Using this blitz you can do the mission in less than 10 minutes, easily.

For ships with high alpha strike: if you group your turrets/launchers and kill a mine in one volley, it will not spawn any NPCs. Mines have 1200 hp each. Using this blitz you can complete the mission in two minutes in absolute safety.

Note: For the salvagers: If you kill every single mine (4 drone bc spawns each) it accumulates to around 50 or so wrecks with drone minerals

You warp in the first pocket using an accelleration gate, no aggro on warp in. There are 3 groups, with increasingly larger size ships, all faction (so no bounty). The 2 groups closest to you (40km and 80km) can be pulled or sniped. If you need to get closer to the 3rd group to pull them (120km) they will aggro you when you are 80 to 90km away. This means you can't get to the next gate without getting attacked by the battleships.